Macdonald Conjectures
Macdonald (1982) extended the conjecture to arbitrary finite or affine root systems, with Dyson's original conjecture corresponding to the case of the An−1 root system and Andrews's conjecture corresponding to the affine An−1 root system. Macdonald reformulated these conjectures as conjectures about the norms of Macdonald polynomials. Macdonald's conjectures were proved by (Cherednik 1995) using doubly affine Hecke algebras.
Macdonald's form of Dyson's conjecture for root systems of type BC is closely related to Selberg's integral.
Read more about this topic: Dyson Conjecture
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